Inclusion Criteria:

• Subject has histologically confirmed diagnosis of advanced (loco-regionally recurrent and not amenable to curative therapy, or metastatic (stage IV)) TNBC.
• Subject has either a measurable disease per RECIST 1.1 criteria or, if no measurable disease is present, then at least one predominantly lytic bone lesion or mixed lytic-blastic bone lesion with identifiable soft tissue component (that can be evaluated by CT/MRI) must be present Part B1: patients must have measurable disease.
• Subject has adequate tumor tissue to identify the PIK3CA mutation status (either carrying a mutation or without a mutation) and the PTEN loss status; both of which will determine whether the subject can be allocated to Part A
• PIK3CA mutation regardless of PTEN status; or to Part B.
• PTEN loss without a PIK3CA mutation.
• Subject has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• Subject has received no more than one line of therapy for metastatic disease.
• Subject has adequate bone marrow and organ function

Exclusion Criteria:

• Subject has received prior treatment with any PI3K, mTOR or AKT inhibitor.
• Subject has a known hypersensitivity to alpelisib, nab-paclitaxel or to any of their excipients.
• Subject has not recovered from all toxicities related to prior anticancer therapies to NCI CTCAE version 4.03 Grade ≤ 1; with the exception of alopecia.
• Subject has central nervous system (CNS) involvement.
• Subject with an established diagnosis of diabetes mellitus type I or uncontrolled type II based on Fasting Plasma Glucose and HbA1c.
• Subject has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection) based on investigator discretion.
• Subject has a history of acute pancreatitis within 1 year of screening or past medical history of chronic pancreatitis.
• Subject has currently documented pneumonitis/interstitial lung disease.
• Subject has a history of severe cutaneous reactions, such as Steven-Johnson Syndrome (SJS), erythema multiforme (EM),Toxic Epidermal Necrolysis (TEN) or Drug Reaction with Eosinophilia and Systemic Syndrome (DRESS).
• Subject with unresolved osteonecrosis of the jaw.
• Other protocol-defined inclusion/exclusion criteria apply.